Simple interest on a sum for $18$ months at $14\%$ per annum is $\text{Rs }1365$. What is the value (in $\text{Rs}$) of the sum?

Given parameters:Simple Interest ($\text{SI}$) $=\text{Rs }1365$ Rate ($R$) $=14\%$ per annumTime ($T$) $=18\text{ months}=\frac{18}{12}\text{ years}=1.5\text{ years}$ The formula for Simple Interest is:
$$\text{SI}=\frac{P\times R\times T}{100}$$
Substitute the values:
$$1365=\frac{P\times 14\times 1.5}{100}$$
$$1365=\frac{21P}{100}$$
$$21P=1365\times 100$$
$$P=\frac{136500}{21}$$
$$P=6500$$
The sum is $\text{Rs }6500$.